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The motor of a crane uses power P to lift a steel beam. By what
factor must the motor’s power increase to lift the beam twice as
high in half the time?
Answer
P = mgh / t
P ‘ = mg 2h / [ t/2 ] = 4 mgh / t = 4 P
4 times
We know that
Power = workdone / time
= m g h /
t
Now
P ‘ = m g h’ / t’
Given that h’ = 2 h
t’ = t / 2
Therefore
P ‘ = m g 2h / t/2
= 4
m g h / t
= 4
P
Therefore power increases by four times of intial power
general formula–>P = mgh / t
changed power P ‘ = mg 2h / [ t/2 ] = 4 mgh / t = 4 P
hence,factor must be increased by factor 4.
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